low-temperature properties of a single crystal of magnetite oriented along principal magnetic axes

ELSEVIER Earth and Planetary Science Letters 165 (1999) 229–239

Low-temperature properties of a single crystal of magnetiteoriented along principal magnetic axes

Ozden Ozdemir Ł, David J. Dunlop

Department of Physics, University of Toronto at Mississauga, Mississauga, Ontario L5L 1C6, Canada

Received 3 September 1998; revised version received 23 November 1998; accepted 24 November 1998

Abstract

We have measured saturation induced and remanent magnetizations and induced magnetization as a function of field atlow temperatures, between 300 K and 10 K, on an oriented 1.5-mm single crystal of magnetite. The induced magnetizationcurves along the cubic [001], [1N10], and [110] axes at 10 K have very different approaches to saturation. The crystal is easyto magnetize along [001] but difficult along [1N10] and [110], the hard directions of magnetization for monoclinic magnetite.The temperature dependence of saturation magnetization between the Verwey transition temperature, Tv D 119 K, and 10K is also different along the three axes, indicating that below Tv the crystal has uniaxial symmetry. The room-temperaturesaturation remanence (SIRM) produced along [001] decreases continuously in the course of zero-field cooling, levellingout at the isotropic temperature, Ti D 130 K, where the first magnetocrystalline anisotropy constant becomes zero. At Ti,86% of the initial SIRM was demagnetized. The domain wall pinning responsible for this soft remanence fraction mustbe magnetocrystalline controlled. The remaining 14% of the SIRM is temperature independent between Ti and Tv andmust be magnetoelastically pinned. This surviving hard remanence is the core of the stable magnetic memory. The Verweytransition at 119 K, where the crystal structure changes from cubic to monoclinic, is marked by a discontinuous increase inremanence, indicating that the cubic [001] direction suddenly becomes an easy direction of magnetization. The formationof monoclinic twins may also affect the intensity of remanence below Tv. Reheating from 10 K retraces the cooling curve,with a decrease at Tv back to the original remanence level, which is maintained to 300 K. When SIRM is not along [001],the initial SIRM is larger but the reversible changes across the Verwey transition are much smaller. The SIRM produced at20 K is an order of magnitude larger than the 300 K SIRM, but the only change during warming is a discontinuous andirreversible drop to zero at Tv. 1999 Published by Elsevier Science B.V. All rights reserved.

Keywords: magnetite; Verwey transition; oriented transition; saturation isothermal remanence; monoclinic magnetite

1. Introduction

Magnetite (Fe3O4) has two magnetic transitionsbelow room temperature. At the isotropic point Ti

around 130 K, the first magnetocrystalline anisotropyconstant (K1) passes through zero, causing domain

Ł Corresponding author. Tel.: C1 (905) 828 3829; Fax: C1 (905)828 3717; E-mail: [email protected]

walls to unpin. At the Verwey transition, a crys-tallographic phase transition variously reported tooccur at Tv D 110–125 K, the structure changesfrom cubic to monoclinic. In most previous studies,it has been difficult to separate with certainty themagnetic effects of the two transitions. For example,in the technique of low-temperature demagnetization(LTD), rocks containing magnetite are cooled to 77K and rewarmed to room temperature in zero field

0012-821X/99/$ – see front matter c 1999 Published by Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 2 6 9 - 6

230 O. Ozdemir, D.J. Dunlop / Earth and Planetary Science Letters 165 (1999) 229–239

in order to erase less stable and reliable componentsof remanent magnetization. It is unclear whether allthe loss of remanence is due to the vanishing ofK1 at Ti or whether the change in crystallographicstructure at Tv, accompanied by switching of mag-netic easy axes, also plays a role, perhaps even acontrolling role. In the present study, by using acarefully oriented crystal of magnetite, we have beenable to clearly separate the effects occurring at thetwo transitions.

The inverse technique to LTD is often used foridentifying magnetite in sediments and soils. It con-sists of producing a synthetic remanence (usuallya saturation isothermal remanent magnetization orSIRM) at very low temperature and continuouslymonitoring the remanence in a zero-field warming–recooling cycle to 300 K. A sudden loss of rema-nence in warming through Tv, sometimes with apartial recovery on recooling, is diagnostic of mag-netite. There is usually little if any remanence changearound Ti in this case.

LTD is of considerable interest as a labora-tory cleaning technique in paleomagnetism [1–3].It serves to remove a large part of the remanencedue to loosely pinned domain walls in multidomain(MD) grains, thereby isolating the stable remanence[4]. LTD experiments on synthetic magnetites [5,6],crushed natural magnetites [7], natural single crystals[2,8], and magnetite-bearing rocks [9] have shownthat the surviving remanence (or magnetic mem-ory) after LTD has single-domain (SD) like proper-ties with high coercivities. As would be expected,memory ratios of both SIRM and thermoremanentmagnetization (TRM) increase as the grain size de-creases [6]. Crystal defects that strongly pin domainwalls also increase the memory and its stability. Acomprehensive review appears in Ref. [10].

Recent work has shown that even a large (3 mm)single crystal of magnetite contains distinct SD-likeand MD remanence components [11]. The magneticmemory following LTD has the following properties:(1) the memories of SIRM and TRM have SD-likealternating field (AF) decay curves; (2) the SIRMand TRM memories have practically no unblockingtemperatures below 560ºC; (3) the memory fractionof high-temperature partial TRM also has mainlyblocking temperatures above 565ºC, very similar tothose of the total TRM memory. Crystal defects

and resulting stress centres, rather than separate SDregions in the crystal, seem to be responsible for thestable SD-like memory.

In many of the LTD experiments described above,measurements were made only at room temperature,before and after cycling the sample to 77 K. Inthis approach, the data between 300 K and 77 Kare lost, including the vitally important propertiesat the isotropic point and the Verwey transition. Inthe present study, we therefore continuously mon-itored the remanent and induced magnetizations ofa well-characterized single crystal of magnetite asa function of temperature in both cooling–warmingand warming–cooling cycles between 300 K and 10K. Our purposes were: (1) to clearly separate theisotropic and Verwey transitions and better definetheir temperatures, Ti and Tv; (2) to understand theeffects of crossing Ti and Tv on both room-temper-ature and low-temperature remanence; (3) to docu-ment how the remanences of the high-temperature(cubic) and low-temperature (monoclinic) phases ofmagnetite change with temperature after crossingthe transitions; and (4) to understand the origin ofthe SD-like magnetic memory of cubic magnetiteat room temperature after an LTD cooling–heatingcycle.

Our experiments were carried out on a pure,stoichiometric natural single crystal of magnetite,carefully oriented so that the magnetic field wasapplied along crystallographic principal axes. Thecrystal quality and purity significantly affect thecrystallographic phase transition. Slight deviationsfrom stoichiometry [12] and the presence of cationimpurities [13,14] cause broadening and eventualsuppression of the Verwey transition. The remanenceand other magnetic properties of magnetite also de-pend strongly on crystallographic orientation. Uponcooling through Tv, the structure changes from cubicspinel to monoclinic. At the same time, the easy di-rections of magnetization change from <111> to oneof the <001> axes.

2. Characterization of the crystal andexperimental procedure

Magnetic measurements were carried out on amuseum-quality 1.5 mm octahedral crystal of mag-

O. Ozdemir, D.J. Dunlop / Earth and Planetary Science Letters 165 (1999) 229–239 231

netite. The {111} crystal faces were flat and smooth,with no striations indicative of deformational twin-ning. X-ray diffraction using a Debye–Scherrer cam-era with Cu-Kα radiation and a silicon standard wascarried out on a small chip of the crystal. The spinelunit cell edge was 8:402 š 0:002 A, in good agree-ment with the standard value 8.396 A for magnetite.

The composition of the crystal was determinedusing a Cameco SX-50 electron microprobe. Chipsof the crystal were probed for Fe, O, and sevenother elements. Six 10-second counts were recordedfor each element at each point and metal standardswere referred to before and after each analysis. Eachelement was measured at six different locations. Theanalyses gave 72:36 š 0:23 weight % Fe, close tothe theoretical 73.6%. Oxygen concentration was27:5 š 0:008 weight %. The weight percents of theother elements were very small: Ti, 0:014 š 0:003;Mg, 0:002š 0:002; Al, 0:081 š 0:008; Mn, 0:026š0:004; Cr, 0:009 š 0:003; Ni, 0:005 š 0:004; andCo, 0:002 š 0:003. The crystal is stoichiometricmagnetite with no major impurities.

The Curie temperature, Tc D 575ºC, was deter-mined from the temperature dependence of weak-field susceptibility measured by a Kappa bridge. Acontinuous jet of argon inhibited chemical alterationduring heating.

Induced magnetization M , saturation magnetiza-tion Ms, and saturation isothermal remanent magne-tization (SIRM) Mrs were measured at low tempera-ture using a Quantum Design MPMS2 magnetometerwith a SQUID detector. Below the Verwey transition(around Tv D 120 K), magnetite is monoclinic, its a,b and c axes corresponding to the [1N10], [110] and[001] directions of cubic magnetite above Tv [15].Our crystal was oriented successively along thesethree principal axes for measurements. The c axisis the direction of easiest magnetization below Tv;a and b are hard and intermediate directions. Themonoclinic c axis may develop in any of the threeequivalent <001> axes. A pre-determined c axis wasobtained by cooling through Tv in a field of 2.5 Tapplied along [001].

After the low-temperature experiments were com-pleted, room-temperature hysteresis was measuredwith a Micro VSM. The room-temperature value ofMs was 93.6 A m2=kg, as for pure magnetite. Thecoercive force Hc was 0.11 mT. The ratios Mrs=Ms

and Hcr=Hc (Hcr is remanent coercive force) were0.002 and 47, respectively. These values, togetherwith the ramp-like form of the hysteresis curve, arediagnostic of multidomain grains containing a largenumber of domain walls.

3. Experimental results

3.1. Induced magnetization curves along principalaxes

Fig. 1 shows induced magnetization M as a func-tion of applied field H measured at 10 K alongthe a, b, and c principal axes. The three magne-tization curves have quite different approaches tosaturation. Saturation was achieved in relatively lowfields of ³0.2 T in the [001] easy direction but re-quired much higher fields in the [1N10] and [110]directions perpendicular to the c axis. Thus the crys-tal below Tv has essentially uniaxial symmetry. Themagnetization curves along the three principal axescan be explained in terms of large magnetocrys-talline anisotropy constants. From torque curvesmeasured at 4.2 K, Abe et al. [16] calculated theanisotropy constants of monoclinic magnetite to beKa D 25:5 ð 104 J=m3, Kb D 3:7 ð 104 J=m3, andKu D 2:1ð 104 J=m3.

3.2. Temperature dependence of saturationmagnetization Ms

The temperature dependences Ms.T / measuredparallel to [001], [1N10], and [110] during coolingfrom 300 K to 10 K in H D 2 T are shown in Figs. 2and 3. In all three crystallographic orientations, Ms

increases with decreasing T according to a .Tc �T /0:4 relation between 300 K and Tv D 119 K. Thenearly identical curves show that cubic magnetiteis magnetically isotropic in fields ½2 T above theVerwey transition.

Below Tv, the Ms.T / curves are different for dif-ferent crystallographic directions. In cooling throughthe Verwey transition, Ms abruptly decreases by1.6% and 1.2% for fields applied along [1N10] and[110], respectively. The field of 2 T applied duringcooling was not enough to saturate the magnetiza-tion along these axes below Tv, as seen earlier in


Fig. 1. Induced magnetization M for magnetic field H applied along [1N10] (monoclinic a axis), [110] (b axis), and [001] (c axis)directions of the magnetite crystal at 10 K.

Fig. 1. These results clearly show that the mag-netocrystalline anisotropy of monoclinic magnetitebelow Tv is much greater than the anisotropy ofcubic magnetite above Tv.

Along [001], the 2 T field is very nearly suffi-cient to saturate the magnetization of the monoclinicphase, and the Ms.T / curve has only a tiny discon-tinuity of ³0.1% at the Verwey transition. However,the slope dMs=dT changes, being lower below Tv.Similar decreases in Ms at the Verwey transitionwere reported by Uemura and Iida [17] and Matsuiet al. [18]. Our measured value of Ms at 10 K is98.65 A m2=kg or 4.09 ¼B per formula unit, in goodagreement with the theoretical value of 4.0 ¼B performula unit at 0 K [19].

3.3. SIRM cooling and rewarming: oriented crystal

The crystal was given an SIRM parallel to [001]in a field of 2.5 T at room temperature, then cooledto 10 K and back to 300 K in zero field (Fig. 4).The remanence decreased steadily with cooling tothe isotropic temperature, Ti D 130 K, where the firstmagnetocrystalline anisotropy constant K1 becomes

zero. At Ti, 86% of the initial SIRM had beendemagnetized. Between Ti and the Verwey transitionat Tv D 119 K, there was no further demagnetization:the residual 14% of the original SIRM remainedconstant.

These observations indicate a sharp separationbetween the two remanence transitions, at Ti andTv, which has not been clear in previously publisheddata on unoriented crystals. In cooling to Ti, the mag-netocrystalline anisotropy decreases to nearly zero;loosely pinned domain walls move as a result, caus-ing a large loss of remanence. Then at Tv D 119 K,there is a crystallographic phase transition in whichmagnetite transforms from cubic to monoclinic. Anabrupt increase in the remanence in cooling throughTv (Fig. 4) indicates that [001], the monoclinic caxis, has suddenly become an easy direction of mag-netization. In crossing the Verwey transition, theremanence increased more than an order of magni-tude, from 0.005 to 0.081 A m2=kg, which is about35% higher than the initial SIRM at 300 K.

In further cooling below Tv, the remanence de-creased about 10% until 70 K, then remained es-sentially constant between 70 K and 10 K. The


Fig. 2. Temperature dependence of saturation magnetization Ms parallel to [1N10] and [110] (a and b axes, respectively) during coolingfrom 300 K to 10 K in a field H D 2 T. The discontinuous drop at the Verwey transition temperature, Tv D 119 K, is evidence of thehigh a- and b-axis anisotropy of the low-temperature monoclinic phase of magnetite.

remanence at 10 K was 0.0695 A m2=kg, still anorder of magnitude higher than the remanence at Ti

or just above Tv.As the crystal was warmed from 10 K, the re-

manence retraced the cooling curve, peaking justbelow Tv and then decreasing dramatically to 0.007A m2=kg in crossing the Verwey transition. Thusthe process or processes affecting the remanence ofthe monoclinic magnetite below Tv are perfectly re-versible. No permanent demagnetization is involved.Furthermore, the remanence recovered by the cu-bic magnetite above Tv is virtually identical to theremanence before cooling through Tv and remainsconstant in heating to 300 K. There is no recoveryof remanence at or above Ti. It is clear that all ir-reversible change in the remanence occurred duringzero-field cooling to Ti. The ultimate SIRM mem-ory at 300 K is completely unaffected by the large,but reversible, changes in the cooling–heating cyclebelow Ti. Thus low-temperature demagnetization is

governed entirely by the vanishing of magnetocrys-talline anisotropy at the isotropic temperature and areunaffected by changes in crystallographic structureat the Verwey transition. Although the two transi-tions are only about 10 K apart, they are distinct andhave quite different effects on remanence.

3.4. SIRM cooling and rewarming: unorientedcrystal

A new SIRM was produced by applying a 2.5T field at room temperature with the crystal unori-ented. The subsequent zero-field cooling and reheat-ing curves are illustrated in Fig. 5. In cooling from300 K to Tv, the remanence of the unoriented crystaldecreased in the same way as that of the orientedcrystal (Fig. 4). However, the unoriented crystal hada 20% higher SIRM intensity. This difference arisesbecause in the oriented crystal, the field was ap-plied along [001], a hard direction of magnetization


Fig. 3. Ms –T curve along the cubic [001] direction (monoclinic c axis) of the crystal during cooling from 300 K to 10 K in a field H D2 T. There is hardly any discontinuity in Ms in crossing the Verwey transition because the anisotropy is much less along the c axis thanalong the a or b axes below Tv.

for cubic magnetite. In a randomly oriented crystal,<111> easy axes are closer to the field direction andconsequently the SIRM is larger.

By 119 K, 89% of the initial SIRM had been de-stroyed. This soft fraction, carried by weakly pinneddomain walls, is almost the same as in the orientedcrystal (Fig. 4). However, the isotropic point is notas clearly separated from the Verwey transition as itwas for the oriented crystal.

Cooling below Tv resulted in a sudden increasein remanence (119–110 K), followed by a smaller,more gradual decrease (110–100 K). Both changeswere repeated exactly in heating from 10 K. Al-though the cooling and reheating curves below Tv

are similar in shape to those of the oriented crystal,the remanence increase across the Verwey transitionis a factor 6 smaller and is spread over a widertemperature interval. The very large, step-like rema-nence increase in the oriented crystal occurs because[001] becomes an easy axis below Tv and the entireremanence is oriented in this direction. In the unori-ented crystal, the domains reorient themselves along

three orthogonal <001> axes, each with only a smallcomponent of magnetization in the measurement di-rection.

In reheating above Tv, the remanence does notretrace the cooling curve but is almost temperatureindependent. The heating and cooling curves do notmatch between Tv and Ti as they did for the orientedcrystal. The SIRM memory at room temperatureis about 11%. Similar SIRM cooling and warmingcurves with some remanence rebound across thetransition have been observed for other unorientedsingle crystals of magnetite [4].

3.5. SIRM warming curve for the oriented crystal

The oriented crystal was given a new SIRM at 20K by applying a 2.5 T field along the monoclinicc-axis, i.e., the cubic [001] direction. It was thenwarmed in zero field to 300 K (Fig. 6). The be-haviour was much simpler than in cooling of room-temperature SIRM. The remanence was almost con-stant between 20 K and 100 K. Just below and at Tv,


Fig. 4. Temperature dependence of saturation remanence (SIRM) MSIRM, produced by a 2.5 T field along [001] at 300 K, duringzero-field cooling from 300 K to 10 K and zero field warming back to 300 K. The magnetic isotropic point at Ti D 130 K and theVerwey transition at Tv D 119 K are cleanly separated in the data. All irreversible loss of remanence occurs between 300 K and Ti;there is no further change between Ti and Tv. There is a large but reversible jump in remanence intensity at Tv when the cubic [001]hard direction becomes the monoclinic c axis, the direction of easy magnetization. Notice that the SIRM cooling and heating curves areirreversible for the high-temperature cubic phase but completely reversible at all temperatures below Tv for the monoclinic phase.

Fig. 5. The zero-field cooling and warming curves of SIRM for the same magnetite crystal when it is magnetized and its remanencemeasured in an arbitrary orientation with respect to the principal crystallographic axes. The effects of Ti and Tv on the remanence cannotbe clearly separated for the unoriented crystal.


Fig. 6. Zero-field SIRM warming curve from 20 K to 300 K for the same magnetite crystal. SIRM was produced in a field of 2.5 T at 20K along the monoclinic c axis (cubic [001]). The behaviour is simple in this case: the remanence, which is about 30 times stronger thanthe room-temperature SIRM in Fig. 4, is constant below Tv then decreases to zero in crossing the Verwey transition.

the remanence decreased essentially to zero, whereit remained in warming to 300 K. Thus SIRM pro-duced at low temperature in monoclinic magnetiteis completely demagnetized in the transition to thecubic phase and no memory of the original SIRM isrecovered in recooling through Tv, in our crystal atleast. This behaviour is entirely different from that ofroom-temperature SIRM cycled to low temperatureand back to 300 K (Fig. 4).

The sharp decrease in remanence at Tv in theSIRM warming curve is diagnostic of stoichiomet-ric magnetite and has been observed previously forreduced submicron magnetites [12]. Our measuredvalue of 119 K for Tv agrees well with previousdeterminations for stoichiometric magnetite crystals[20–22]. A striking result in Fig. 6 is the high inten-sity of low-temperature SIRM: 1.45 A m2=kg, about30 times higher than room-temperature SIRM. Partof the difference is due to the fact that [001] is themonoclinic easy axis but a cubic hard axis. However,to explain such a large contrast, there must be quitedifferent domain configurations in the SIRM state at20 K and 300 K. The high uniaxial anisotropy of thelow-temperature monoclinic phase must pin domainwalls much farther from their equilibrium positions.

4. Discussion

Cooling our crystal in zero field through theisotropic point at Ti D 130 K resulted in the per-manent loss of 86% of the room-temperature SIRM(Fig. 4). This decrease in remanence with coolingbelow 300 K is mainly due to progressive jumps ofloosely pinned domain walls [4]. According to Kittel[23], the 180º Bloch wall thickness w is given by

w D ³.A=Ku/1=2 (1)

where A is the exchange constant and Ku is the ef-fective magnetic anisotropy, which is the sum of themagnetocrystalline and magnetoelastic anisotropies[24]:

Ku D �.2=3/K1 C .9=2/c44½2111 (2)

Since K1, ½111 and c44 all decrease with decreas-ing temperature (apart from a minor increase in K1

just below room temperature), the wall thickness be-low room temperature increases with cooling. Broadwalls are less effectively pinned by localized defectsand eventually escape. At 130 K, K1 becomes zeroand changes sign. Domain walls blocked by magne-tocrystalline controlled pinning become free to jump


and lead to demagnetization of a large fraction ofremanence. These loosely pinned walls are also eas-ily moved by alternating fields or heating. Ozdemirand Dunlop [11] found that the fraction of rema-nence erased by LTD in a large crystal of magnetitehad low coercivities and a broad spectrum of lowunblocking temperatures.

The remaining 14% of the room-temperatureSIRM was not destroyed by cycling through Ti. Evencycling through Tv had no effect on this SIRM mem-ory, which is due to strongly pinned domain walls,probably pinned magnetostrictively by dislocationsor other crystal defects. Although K1 becomes zeroand changes sign at the isotropic point, ½111, ½100,and c44 are not zero, making an important contri-bution to the magnetoelastic anisotropy that controlsthe magnetic memory. These walls are so stronglypinned by the stress fields of crystal defects that theremanence they carry is independent of temperatureduring reheating from Ti to 300 K (Fig. 4). Thispinning may explain the SD-like memories observedin small and large MD magnetites [2,5,6]. Ozdemirand Dunlop [11] found that the memories of TRM,partial TRM, and SIRM of 3-mm and 4.5-mm mag-netite crystals had SD-like AF decay curves withinitial plateaus of no demagnetization and thermaldemagnetization curves with no unblocking temper-atures below 560ºC.

The hardness of the SD-like remanence was at-tributed to the strong pinning of walls by defectconcentrations at monoclinic twin boundaries [11].However, Fig. 4 clearly indicates that the cubic !monoclinic transition occurs ³10 degrees below theisotropic point, and the memory is temperature in-dependent between Ti and Tv. Although monoclinictwinning probably plays an important role in con-trolling the remanence below the Verwey transition,it has no effect on the memory of cubic magnetiteabove Tv. On the other hand, if the SIRM is impartedat low temperature and the Verwey transition is ap-proached from below, a major part of the remanenceis lost at Tv and there is no indication of any furtherchange at Ti (Fig. 6). Most of the decrease at Tv ispermanent, with almost no recovery in the secondcrossing of the Verwey transition in the cooling halfof the cycle.

The room-temperature SIRM behaves in a com-pletely different way as the Verwey transition is

approached from above, crossed, and then recrossedin the warming half of the cycle. Although there isagain a sudden large change in remanence at Tv inthe first crossing (in this case an increase), the effectis completely reversible (Figs. 4 and 5). In recrossingthe transition, the remanence reverts to its originallevel.

The discontinuous change in remanence is muchmore pronounced when the crystal is oriented sothat SIRM is produced and measured along [001],which becomes the c axis of the monoclinic phasebelow Tv. One reason for this is the following. Since[001] is a hard axis above Tv, the domains thatcarry the SIRM have a choice of four equivalent<111> easy directions, which make identical anglesof 54.7º with [001] and are arranged symmetricallyabout [001]. These domain magnetizations are to aconsiderable extent mutually cancelling, leading toa relatively small SIRM. However, in crossing Tv,[001] becomes the monoclinic easy axis and all thedomain magnetizations rotate into this direction. Theremanence increases accordingly. In recrossing thetransition, the domain magnetizations revert to theinitial set of equally spaced <111> directions and theremanence drops back to its original level.

When the crystal is not oriented along [001], oneof the <111> directions is necessarily closer to thefield direction than the others and is preferred by thedomain magnetizations. The SIRM will be larger,as we observe, but the change across the Verweytransition will be less (Fig. 5), for two reasons. First,the remanence below Tv cannot be as large as inthe crystal oriented along the monoclinic easy axis.Second, it is not certain that only one of the set of<001> axes is chosen as the c-axis throughout theunoriented crystal, so that the domains may have achoice of competing magnetization directions belowTv. Indeed monoclinic twinning is well establishedin magnetite. In assemblages of randomly orientedMD crystals, for example glass–ceramic magnetites[4], so many competing directions are available thatno increase is observed across the transition.

This general explanation assumes that domainwalls remain pinned in the same positions in cross-ing the Verwey transition, with only the directionsof the domain magnetizations changing. However,this model can only account for a remanence in-crease of 1= cos 54:7º D 1:73 at most, and the in-


crease in Fig. 4 is much larger than this. Thereforethe discontinuous change in remanence is proba-bly controlled in part by discontinuous changes inmagnetic anisotropy, magnetostriction, and magne-toelastic constants due to the switching of the easyaxes at Tv. The magnetic anisotropy constants of thelow-temperature phase of magnetite are expressed interms of Ka , Kb, Ku, Kaa , Kbb, and Kab [25]. Theyare all positive and temperature dependent. Abe etal. [16] calculated the thermal variation of K1 valuesand showed that the K1(T) curve has a discontin-uous increase at the Verwey transition. The tem-perature variations of the magnetostriction constants½111, ½100 and ½s also show abrupt changes at thephase transition [22]. Moran and Lutfi [26] measuredthe temperature dependence of c44, which likewiseexhibits a discontinuous increase at the phase tran-sition. According to Eqs. 1 and 2, any increases inmagnetocrystalline, magnetostriction, and magnetoe-lastic constants at Tv will result in a decrease in thedomain wall thickness. Then the domain walls willbe very efficiently pinned by internal stresses due tocrystal defects. This does not of itself explain theobservations in Fig. 4, however, because walls mustmove in order to accomplish a further increase inremanence.

Another factor controlling the remanence belowTv is the presence of monoclinic twin boundaries(TWB). As the crystal cools through Tv, it acquiresa twin structure [16,18,20,27]. Electron microscopeobservations at 77 K show two kinds of TWB’sbetween monoclinic twins with orthogonal c axes.One type of TWB is perpendicular to one of the caxes, and the other makes a 45º angle with both caxes [27]. Twinning of the monoclinic crystal withrespect to the orientation of the a and b axes intro-duces strain at the TWB’s [28]. The twin junctionsbecome regions of maximum strain which can actas pinning centres for domain walls. Wall pinningat the TWB’s must be strong enough to bring theremanence to a peak value of 0.08 A m2=kg, whichis an order of magnitude higher than the value justabove Tv. As the crystal is warmed, the process is re-versed. At Tv, the monoclinic TWB’s will disappear,resulting in domain wall unpinning and a suddendecrease in remanence. In Fig. 4, the cooling andwarming curves coincide within the accuracy of thedrawing. This is consistent with the reversible ap-

pearance of TWB’s upon cooling across Tv and theirdisappearance on subsequent heating.

5. Conclusions

SIRM cooling=rewarming curves provide impor-tant information about low-temperature demagneti-zation (LTD). LTD destroys remanence due to theloosely pinned domain walls (magnetocrystallinepinning), leaving strongly pinned walls (magnetoe-lastic pinning) and possibly other sources of rema-nence as the carriers of low-temperature memory.All unpinning occurs at Ti in our crystal.

There is a clean separation between the two rema-nence transitions in our magnetite crystal. The mag-netic isotropic point, where the first magnetocrys-talline anisotropy constant passes through zero, is atTi D 130 K. The Verwey transition, at which thecrystal structure changes from cubic to monoclinic,occurs at Tv D 119 K.

The shapes of the remanence curves and othermagnetic properties at temperatures below and abovethe Verwey transition depend strongly on the crystal-lographic orientation of the crystal.

When the crystal is cooled below the Verweytransition, the crystal is more difficult to magnetizeto saturation along the a and b axes, which arethe hard and medium directions of magnetization.The crystal is much easier to magnetize along thec-axis (cubic [001] direction). These observations(Fig. 1) indicate that the magnetic symmetry hasbeen reduced from cubic to uniaxial at Tv.

Monoclinic twin formation just below the Verweytransition has a significant effect on the hardnessand intensity of SIRM. The twin boundaries interactstrongly with the domain walls and tend to act aswall pinning sites.

Room-temperature and low-temperature SIRM’sbehave entirely differently in thermal cycles acrossthe Verwey transition. Low-temperature SIRM dropsirreversibly to almost zero in heating across Tv,with very little recovery in the second crossing.High-temperature SIRM increases sharply in coolingacross Tv, but the behaviour at and below Tv is com-pletely reversible and the original remanence level isrecovered in the second crossing. Warming a low-temperature SIRM pinpoints the Verwey transition


and is a good method of identifying magnetite, but itgives no information about remanence changes nearthe isotropic point Ti.

Acknowledgements

We thank Malcolm Back of the Royal OntarioMuseum, Toronto for donating the natural singlecrystal of magnetite and Sue Halgedahl and RonMerrill for helpful reviews. These measurementswere carried out at the Institute for Rock Magnetismat the University of Minnesota, which is operatedwith funding from the National Science Foundationand the Keck Foundation. We are grateful to Drs.Subir Banerjee and Bruce Moskowitz for welcomingus Visiting Fellows and to Jim Marvin and MikeJackson for help with the instruments. [RV]

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low-temperature properties of a single crystal of magnetite oriented along principal magnetic axes

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